Problem: Simplify the following expression: $k = \dfrac{2a^2 - 14a - 16}{a - 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ k =\dfrac{2(a^2 - 7a - 8)}{a - 8} $ Then we factor the remaining polynomial: $a^2 {-7}a {-8} $ ${-8} + {1} = {-7}$ ${-8} \times {1} = {-8}$ $ (a {-8}) (a + {1}) $ This gives us a factored expression: $\dfrac{2(a {-8}) (a + {1})}{a - 8}$ We can divide the numerator and denominator by $(a + 8)$ on condition that $a \neq 8$ Therefore $k = 2(a + 1); a \neq 8$